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1st order of transformation

shift left or right

2nd order of transformation

stretch or compress horizontally

3rd order of transformation

reflect about the y-axis

4th order of transformation

stretch or compress vertically

5th order of transformation

reflect about the x-axis

Last order of transformation

shift up or down

Shifted upwards

When graph of y = f(x) + k

Shifted downwards

When graph of y = f(x) - k

Shift to the left

When graph of y = f(x + h)

Shift to the right

When graph of y = f(x - h)

Vertical compression

y = af(x) is the graph of y = f(x) compress vertically by a factor of |a| units if |a| < 1

Vertical stretch

y = af(x) is the graph of y = f(x) stretch vertically by a factor of |a| units if |a| > 1

Horizontal compression

y = f(cx) is the graph of y = f(x) compressed horizontally by a factor of |1/c| units if |c| > 1

Horizontal stretch

y = f(cx) is the graph of y = f(x) stretched horizontally by a factor of |1/c| units if |c| < 1

Reflected about the x-axis

Graph of y = -f(x) is the graph y = f(x)

Reflected about the y-axis

Graph of y = f(-x) is the graph of y = f(x)